[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:A. \:\: 10[/tex]
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[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: {x}^{2} + \cfrac{1}{ {x}^{2} } = 102[/tex]
[ subtract 2 from both sides ]
[tex]\qquad \tt \rightarrow \: {x}^{2} + \cfrac{1}{ {x}^{2} } - 2 = 102 - 2[/tex]
[tex]\qquad \tt \rightarrow \: {x}^{2} + \cfrac{1}{ {x}^{2} } - \bigg( 2 \sdot x \sdot \cfrac{1}{x} \bigg)= 100[/tex]
[ 2 can written like that, as they cancel out each other ]
Apply Identity [ a² + b² -2ab = (a - b)² ]
[tex]\qquad \tt \rightarrow \: \bigg (x - \cfrac{1}{x} \bigg) {}^{2} = 100[/tex]
[tex]\qquad \tt \rightarrow \: x - \cfrac{1}{x} {}^{} = \sqrt{100}[/tex]
[tex]\qquad \tt \rightarrow \: x - \cfrac{1}{x} {}^{} = 10[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
